solve the equation by using the elimination method.

Question

2x - 4y = 10

-2x + 6y = -4

Answer 1

The first thing we want to do when we solve by elimination is to line up the variables:

2x-4y=10

-2x+6y=-4

Now, we think about if we add or subtract both equations together, can we have one of the variables be equal to 0? Our goal is to have a variable be eliminated.

In this case, we have 2x and -2x in the two equations. If we add these together, -2x+2x=0x

When we add both equations together we get:

2x-4y=10

+(-2x+6y=-4)

= 0x+2y=6

Now solve for y:

2y=6

y=3 (divide both sides by 2)

Now we have our y value, but a solution to a system of equations requires x and y. Now we can plug in our y value into one of the original equations. I will choose the first equation.

2x-4y=10

2x-4(3)=10

2x-12=10

2x=22 (add 12 to both sides)

x=11 (divide both sides by 2)

So we get:

x=11 and y=3

Answer 2

Look for coefficients of the x and y terms (those are the numbers in front of x and y!) that have the same numbers, but opposite signs.

In this case you're in luck, because the coefficient of x in equation 1 is 2, and the coefficient of x in equation 2 is -2.

The next step is to add the two equations. The terms with same numbers, opposite signs should cancel, and you've eliminated a variable! Solve for the remaining variable, and then substitute your answer back into one of the equations.

Answer 3

2x - 4y = 10

-2x + 6y = -4

Add the two equations and get

2y = 6

y = 3

Now plug this value of y into either equation and solve for x. You should be able to finish from here.

Answer 4

Hi there! I'd love to help you out:

2x - 4y = 10

-2x + 6y = -4 The x's cancel and add the other parts of the equations

2y = 6 Divide by 2

/2 /2

y = 3 Plug 3 in for y in one of the original equations

2x -4(3) = 10

2x-12=10

+12 +12

2x = 22

/2 /2

x = 11

There you have it! I hope this explanation was thorough and answered all of your questions. If you have any additional questions don't hesitate to reach out. Learn on! :)